Abstract

Transient four-wave mixing signals were observed in cold sodium atoms. This phenomenon is interpreted as Bragg diffraction of a probe pulse by a population grating of the ground-state hyperfine level induced by pump pulses. The decay time of this grating is directly related to the temperature of the cold atoms and can serve as a novel technique for temperature diagnostics.

© 1998 Optical Society of America

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  1. E. L. Raab, M. Prentiss, A. Cable, S. Chu, and D. E. Pritchard, Phys. Rev. Lett. 59, 2631 (1987).
    [CrossRef] [PubMed]
  2. D. Grison, B. Lounis, C. Salmon, J. Y. Courtois, and G. Grynberg, Europhys. Lett. 15, 149 (1991).
    [CrossRef]
  3. L. Hilico, C. Fabre, and E. Giacobino, Europhys. Lett. 18, 685 (1992).
    [CrossRef]
  4. J. W. R. Tabosa, G. Chen, Z. Hu, R. B. Lee, and H. J. Kimble, Phys. Rev. Lett. 66, 3245 (1991).
    [CrossRef] [PubMed]
  5. M. Mitsunaga, T. Mukai, K. Watanabe, and T. Mukai, J. Opt. Soc. Am. B 13, 2696 (1996).
    [CrossRef]
  6. A. Lambrecht, E. Giacobino, and J. M. Courty, Opt. Commun. 115, 199 (1995).
    [CrossRef]
  7. A. Lambrecht, T. Coudreau, A. M. Steinberg, and E. Giacobino, Europhys. Lett. 36, 93 (1996).
    [CrossRef]
  8. J.-F. Roch, K. Vigneron, Ph. Grelu, A. Sinatra, J.-Ph. Poizat, and Ph. Grangier, Phys. Rev. Lett. 78, 634 (1997).
    [CrossRef]
  9. J. W. R. Tabosa, S. S. Vianna, and F. A. M. de Oliveira, Phys. Rev. A 55, 2968 (1997).
    [CrossRef]
  10. R. M. Macfarlane and R. M. Shelby, in Spectroscopy of Solids Containing Rare Earth Ions, A. A. Kaplyanskii and R. M. Macfarlane, eds. (North-Holland, Amsterdam, 1987).
  11. M. Mitsunaga, N. Uesugi, H. Sasaki, and K. Karaki, Opt. Lett. 19, 752 (1994).
    [CrossRef] [PubMed]
  12. The ?10?cm mean free path of the Na atom in a MOT is much larger than the cloud size.?Also, the effects of the forces of gravity and the ?10?G/cm magnetic-field gradient on atoms in a MOT are both negligible at the time scale of interest.
  13. See, for example, H. J. Eichler, P. Günter, and D. W. Pohl, Laser-Induced Gratings (Springer-Verlag, Berlin, 1986).
    [CrossRef]
  14. D. W. Phillion, D. J. Kuizenga, and A. E. Siegmann, Appl. Phys. Lett. 27, 85 (1975).
    [CrossRef]
  15. D. S. Chemla, D. A. B. Miller, P. W. Smith, A. C. Gossard, and W. Wiegmann, IEEE J. Quantum Electron. QE-20, 265 (1984).
    [CrossRef]
  16. M. Mitsunaga, H. Shinojima, and K. Kubodera, J. Opt. Soc. Am. B 5, 1448 (1988).
    [CrossRef]
  17. This FWM should be distinguished from Bragg diffraction in optical lattices, in which the atoms are confined to only the lattice points; see, for example, G. Raithel, G. Birkl, A. Kastberg, W. D. Phillips, and S. L. Rolston, Phys. Rev. Lett. 78, 630 (1997).
    [CrossRef]
  18. M. A. Joffe, W. Ketterle, A. Martin, and D. E. Pritchard, J. Opt. Soc. Am. B 10, 2257 (1993).
    [CrossRef]
  19. P. D. Lett, R. N. Watts, C. I. Westbrook, W. D. Phillips, P. L. Gould, and H. J. Metcalf, Phys. Rev. Lett. 61, 169 (1988).
    [CrossRef] [PubMed]
  20. C. D. Wallace, T. P. Dinneen, K. Y. N. Tan, A. Kumarakrishnan, P. L. Gould, and J. Javanainen, J. Opt. Soc. Am. B 11, 703 (1994).
    [CrossRef]

1997 (3)

J.-F. Roch, K. Vigneron, Ph. Grelu, A. Sinatra, J.-Ph. Poizat, and Ph. Grangier, Phys. Rev. Lett. 78, 634 (1997).
[CrossRef]

J. W. R. Tabosa, S. S. Vianna, and F. A. M. de Oliveira, Phys. Rev. A 55, 2968 (1997).
[CrossRef]

This FWM should be distinguished from Bragg diffraction in optical lattices, in which the atoms are confined to only the lattice points; see, for example, G. Raithel, G. Birkl, A. Kastberg, W. D. Phillips, and S. L. Rolston, Phys. Rev. Lett. 78, 630 (1997).
[CrossRef]

1996 (2)

M. Mitsunaga, T. Mukai, K. Watanabe, and T. Mukai, J. Opt. Soc. Am. B 13, 2696 (1996).
[CrossRef]

A. Lambrecht, T. Coudreau, A. M. Steinberg, and E. Giacobino, Europhys. Lett. 36, 93 (1996).
[CrossRef]

1995 (1)

A. Lambrecht, E. Giacobino, and J. M. Courty, Opt. Commun. 115, 199 (1995).
[CrossRef]

1994 (2)

1993 (1)

1992 (1)

L. Hilico, C. Fabre, and E. Giacobino, Europhys. Lett. 18, 685 (1992).
[CrossRef]

1991 (2)

J. W. R. Tabosa, G. Chen, Z. Hu, R. B. Lee, and H. J. Kimble, Phys. Rev. Lett. 66, 3245 (1991).
[CrossRef] [PubMed]

D. Grison, B. Lounis, C. Salmon, J. Y. Courtois, and G. Grynberg, Europhys. Lett. 15, 149 (1991).
[CrossRef]

1988 (2)

P. D. Lett, R. N. Watts, C. I. Westbrook, W. D. Phillips, P. L. Gould, and H. J. Metcalf, Phys. Rev. Lett. 61, 169 (1988).
[CrossRef] [PubMed]

M. Mitsunaga, H. Shinojima, and K. Kubodera, J. Opt. Soc. Am. B 5, 1448 (1988).
[CrossRef]

1987 (1)

E. L. Raab, M. Prentiss, A. Cable, S. Chu, and D. E. Pritchard, Phys. Rev. Lett. 59, 2631 (1987).
[CrossRef] [PubMed]

1984 (1)

D. S. Chemla, D. A. B. Miller, P. W. Smith, A. C. Gossard, and W. Wiegmann, IEEE J. Quantum Electron. QE-20, 265 (1984).
[CrossRef]

1975 (1)

D. W. Phillion, D. J. Kuizenga, and A. E. Siegmann, Appl. Phys. Lett. 27, 85 (1975).
[CrossRef]

Birkl, G.

This FWM should be distinguished from Bragg diffraction in optical lattices, in which the atoms are confined to only the lattice points; see, for example, G. Raithel, G. Birkl, A. Kastberg, W. D. Phillips, and S. L. Rolston, Phys. Rev. Lett. 78, 630 (1997).
[CrossRef]

Cable, A.

E. L. Raab, M. Prentiss, A. Cable, S. Chu, and D. E. Pritchard, Phys. Rev. Lett. 59, 2631 (1987).
[CrossRef] [PubMed]

Chemla, D. S.

D. S. Chemla, D. A. B. Miller, P. W. Smith, A. C. Gossard, and W. Wiegmann, IEEE J. Quantum Electron. QE-20, 265 (1984).
[CrossRef]

Chen, G.

J. W. R. Tabosa, G. Chen, Z. Hu, R. B. Lee, and H. J. Kimble, Phys. Rev. Lett. 66, 3245 (1991).
[CrossRef] [PubMed]

Chu, S.

E. L. Raab, M. Prentiss, A. Cable, S. Chu, and D. E. Pritchard, Phys. Rev. Lett. 59, 2631 (1987).
[CrossRef] [PubMed]

Coudreau, T.

A. Lambrecht, T. Coudreau, A. M. Steinberg, and E. Giacobino, Europhys. Lett. 36, 93 (1996).
[CrossRef]

Courtois, J. Y.

D. Grison, B. Lounis, C. Salmon, J. Y. Courtois, and G. Grynberg, Europhys. Lett. 15, 149 (1991).
[CrossRef]

Courty, J. M.

A. Lambrecht, E. Giacobino, and J. M. Courty, Opt. Commun. 115, 199 (1995).
[CrossRef]

de Oliveira, F. A. M.

J. W. R. Tabosa, S. S. Vianna, and F. A. M. de Oliveira, Phys. Rev. A 55, 2968 (1997).
[CrossRef]

Dinneen, T. P.

Eichler, H. J.

See, for example, H. J. Eichler, P. Günter, and D. W. Pohl, Laser-Induced Gratings (Springer-Verlag, Berlin, 1986).
[CrossRef]

Fabre, C.

L. Hilico, C. Fabre, and E. Giacobino, Europhys. Lett. 18, 685 (1992).
[CrossRef]

Giacobino, E.

A. Lambrecht, T. Coudreau, A. M. Steinberg, and E. Giacobino, Europhys. Lett. 36, 93 (1996).
[CrossRef]

A. Lambrecht, E. Giacobino, and J. M. Courty, Opt. Commun. 115, 199 (1995).
[CrossRef]

L. Hilico, C. Fabre, and E. Giacobino, Europhys. Lett. 18, 685 (1992).
[CrossRef]

Gossard, A. C.

D. S. Chemla, D. A. B. Miller, P. W. Smith, A. C. Gossard, and W. Wiegmann, IEEE J. Quantum Electron. QE-20, 265 (1984).
[CrossRef]

Gould, P. L.

C. D. Wallace, T. P. Dinneen, K. Y. N. Tan, A. Kumarakrishnan, P. L. Gould, and J. Javanainen, J. Opt. Soc. Am. B 11, 703 (1994).
[CrossRef]

P. D. Lett, R. N. Watts, C. I. Westbrook, W. D. Phillips, P. L. Gould, and H. J. Metcalf, Phys. Rev. Lett. 61, 169 (1988).
[CrossRef] [PubMed]

Grangier, Ph.

J.-F. Roch, K. Vigneron, Ph. Grelu, A. Sinatra, J.-Ph. Poizat, and Ph. Grangier, Phys. Rev. Lett. 78, 634 (1997).
[CrossRef]

Grelu, Ph.

J.-F. Roch, K. Vigneron, Ph. Grelu, A. Sinatra, J.-Ph. Poizat, and Ph. Grangier, Phys. Rev. Lett. 78, 634 (1997).
[CrossRef]

Grison, D.

D. Grison, B. Lounis, C. Salmon, J. Y. Courtois, and G. Grynberg, Europhys. Lett. 15, 149 (1991).
[CrossRef]

Grynberg, G.

D. Grison, B. Lounis, C. Salmon, J. Y. Courtois, and G. Grynberg, Europhys. Lett. 15, 149 (1991).
[CrossRef]

Günter, P.

See, for example, H. J. Eichler, P. Günter, and D. W. Pohl, Laser-Induced Gratings (Springer-Verlag, Berlin, 1986).
[CrossRef]

Hilico, L.

L. Hilico, C. Fabre, and E. Giacobino, Europhys. Lett. 18, 685 (1992).
[CrossRef]

Hu, Z.

J. W. R. Tabosa, G. Chen, Z. Hu, R. B. Lee, and H. J. Kimble, Phys. Rev. Lett. 66, 3245 (1991).
[CrossRef] [PubMed]

Javanainen, J.

Joffe, M. A.

Karaki, K.

Kastberg, A.

This FWM should be distinguished from Bragg diffraction in optical lattices, in which the atoms are confined to only the lattice points; see, for example, G. Raithel, G. Birkl, A. Kastberg, W. D. Phillips, and S. L. Rolston, Phys. Rev. Lett. 78, 630 (1997).
[CrossRef]

Ketterle, W.

Kimble, H. J.

J. W. R. Tabosa, G. Chen, Z. Hu, R. B. Lee, and H. J. Kimble, Phys. Rev. Lett. 66, 3245 (1991).
[CrossRef] [PubMed]

Kubodera, K.

Kuizenga, D. J.

D. W. Phillion, D. J. Kuizenga, and A. E. Siegmann, Appl. Phys. Lett. 27, 85 (1975).
[CrossRef]

Kumarakrishnan, A.

Lambrecht, A.

A. Lambrecht, T. Coudreau, A. M. Steinberg, and E. Giacobino, Europhys. Lett. 36, 93 (1996).
[CrossRef]

A. Lambrecht, E. Giacobino, and J. M. Courty, Opt. Commun. 115, 199 (1995).
[CrossRef]

Lee, R. B.

J. W. R. Tabosa, G. Chen, Z. Hu, R. B. Lee, and H. J. Kimble, Phys. Rev. Lett. 66, 3245 (1991).
[CrossRef] [PubMed]

Lett, P. D.

P. D. Lett, R. N. Watts, C. I. Westbrook, W. D. Phillips, P. L. Gould, and H. J. Metcalf, Phys. Rev. Lett. 61, 169 (1988).
[CrossRef] [PubMed]

Lounis, B.

D. Grison, B. Lounis, C. Salmon, J. Y. Courtois, and G. Grynberg, Europhys. Lett. 15, 149 (1991).
[CrossRef]

Macfarlane, R. M.

R. M. Macfarlane and R. M. Shelby, in Spectroscopy of Solids Containing Rare Earth Ions, A. A. Kaplyanskii and R. M. Macfarlane, eds. (North-Holland, Amsterdam, 1987).

Martin, A.

Metcalf, H. J.

P. D. Lett, R. N. Watts, C. I. Westbrook, W. D. Phillips, P. L. Gould, and H. J. Metcalf, Phys. Rev. Lett. 61, 169 (1988).
[CrossRef] [PubMed]

Miller, D. A. B.

D. S. Chemla, D. A. B. Miller, P. W. Smith, A. C. Gossard, and W. Wiegmann, IEEE J. Quantum Electron. QE-20, 265 (1984).
[CrossRef]

Mitsunaga, M.

Mukai, T.

Phillion, D. W.

D. W. Phillion, D. J. Kuizenga, and A. E. Siegmann, Appl. Phys. Lett. 27, 85 (1975).
[CrossRef]

Phillips, W. D.

This FWM should be distinguished from Bragg diffraction in optical lattices, in which the atoms are confined to only the lattice points; see, for example, G. Raithel, G. Birkl, A. Kastberg, W. D. Phillips, and S. L. Rolston, Phys. Rev. Lett. 78, 630 (1997).
[CrossRef]

P. D. Lett, R. N. Watts, C. I. Westbrook, W. D. Phillips, P. L. Gould, and H. J. Metcalf, Phys. Rev. Lett. 61, 169 (1988).
[CrossRef] [PubMed]

Pohl, D. W.

See, for example, H. J. Eichler, P. Günter, and D. W. Pohl, Laser-Induced Gratings (Springer-Verlag, Berlin, 1986).
[CrossRef]

Poizat, J.-Ph.

J.-F. Roch, K. Vigneron, Ph. Grelu, A. Sinatra, J.-Ph. Poizat, and Ph. Grangier, Phys. Rev. Lett. 78, 634 (1997).
[CrossRef]

Prentiss, M.

E. L. Raab, M. Prentiss, A. Cable, S. Chu, and D. E. Pritchard, Phys. Rev. Lett. 59, 2631 (1987).
[CrossRef] [PubMed]

Pritchard, D. E.

M. A. Joffe, W. Ketterle, A. Martin, and D. E. Pritchard, J. Opt. Soc. Am. B 10, 2257 (1993).
[CrossRef]

E. L. Raab, M. Prentiss, A. Cable, S. Chu, and D. E. Pritchard, Phys. Rev. Lett. 59, 2631 (1987).
[CrossRef] [PubMed]

Raab, E. L.

E. L. Raab, M. Prentiss, A. Cable, S. Chu, and D. E. Pritchard, Phys. Rev. Lett. 59, 2631 (1987).
[CrossRef] [PubMed]

Raithel, G.

This FWM should be distinguished from Bragg diffraction in optical lattices, in which the atoms are confined to only the lattice points; see, for example, G. Raithel, G. Birkl, A. Kastberg, W. D. Phillips, and S. L. Rolston, Phys. Rev. Lett. 78, 630 (1997).
[CrossRef]

Roch, J.-F.

J.-F. Roch, K. Vigneron, Ph. Grelu, A. Sinatra, J.-Ph. Poizat, and Ph. Grangier, Phys. Rev. Lett. 78, 634 (1997).
[CrossRef]

Rolston, S. L.

This FWM should be distinguished from Bragg diffraction in optical lattices, in which the atoms are confined to only the lattice points; see, for example, G. Raithel, G. Birkl, A. Kastberg, W. D. Phillips, and S. L. Rolston, Phys. Rev. Lett. 78, 630 (1997).
[CrossRef]

Salmon, C.

D. Grison, B. Lounis, C. Salmon, J. Y. Courtois, and G. Grynberg, Europhys. Lett. 15, 149 (1991).
[CrossRef]

Sasaki, H.

Shelby, R. M.

R. M. Macfarlane and R. M. Shelby, in Spectroscopy of Solids Containing Rare Earth Ions, A. A. Kaplyanskii and R. M. Macfarlane, eds. (North-Holland, Amsterdam, 1987).

Shinojima, H.

Siegmann, A. E.

D. W. Phillion, D. J. Kuizenga, and A. E. Siegmann, Appl. Phys. Lett. 27, 85 (1975).
[CrossRef]

Sinatra, A.

J.-F. Roch, K. Vigneron, Ph. Grelu, A. Sinatra, J.-Ph. Poizat, and Ph. Grangier, Phys. Rev. Lett. 78, 634 (1997).
[CrossRef]

Smith, P. W.

D. S. Chemla, D. A. B. Miller, P. W. Smith, A. C. Gossard, and W. Wiegmann, IEEE J. Quantum Electron. QE-20, 265 (1984).
[CrossRef]

Steinberg, A. M.

A. Lambrecht, T. Coudreau, A. M. Steinberg, and E. Giacobino, Europhys. Lett. 36, 93 (1996).
[CrossRef]

Tabosa, J. W. R.

J. W. R. Tabosa, S. S. Vianna, and F. A. M. de Oliveira, Phys. Rev. A 55, 2968 (1997).
[CrossRef]

J. W. R. Tabosa, G. Chen, Z. Hu, R. B. Lee, and H. J. Kimble, Phys. Rev. Lett. 66, 3245 (1991).
[CrossRef] [PubMed]

Tan, K. Y. N.

Uesugi, N.

Vianna, S. S.

J. W. R. Tabosa, S. S. Vianna, and F. A. M. de Oliveira, Phys. Rev. A 55, 2968 (1997).
[CrossRef]

Vigneron, K.

J.-F. Roch, K. Vigneron, Ph. Grelu, A. Sinatra, J.-Ph. Poizat, and Ph. Grangier, Phys. Rev. Lett. 78, 634 (1997).
[CrossRef]

Wallace, C. D.

Watanabe, K.

Watts, R. N.

P. D. Lett, R. N. Watts, C. I. Westbrook, W. D. Phillips, P. L. Gould, and H. J. Metcalf, Phys. Rev. Lett. 61, 169 (1988).
[CrossRef] [PubMed]

Westbrook, C. I.

P. D. Lett, R. N. Watts, C. I. Westbrook, W. D. Phillips, P. L. Gould, and H. J. Metcalf, Phys. Rev. Lett. 61, 169 (1988).
[CrossRef] [PubMed]

Wiegmann, W.

D. S. Chemla, D. A. B. Miller, P. W. Smith, A. C. Gossard, and W. Wiegmann, IEEE J. Quantum Electron. QE-20, 265 (1984).
[CrossRef]

Appl. Phys. Lett. (1)

D. W. Phillion, D. J. Kuizenga, and A. E. Siegmann, Appl. Phys. Lett. 27, 85 (1975).
[CrossRef]

Europhys. Lett. (3)

A. Lambrecht, T. Coudreau, A. M. Steinberg, and E. Giacobino, Europhys. Lett. 36, 93 (1996).
[CrossRef]

D. Grison, B. Lounis, C. Salmon, J. Y. Courtois, and G. Grynberg, Europhys. Lett. 15, 149 (1991).
[CrossRef]

L. Hilico, C. Fabre, and E. Giacobino, Europhys. Lett. 18, 685 (1992).
[CrossRef]

IEEE J. Quantum Electron. (1)

D. S. Chemla, D. A. B. Miller, P. W. Smith, A. C. Gossard, and W. Wiegmann, IEEE J. Quantum Electron. QE-20, 265 (1984).
[CrossRef]

J. Opt. Soc. Am. B (4)

Opt. Commun. (1)

A. Lambrecht, E. Giacobino, and J. M. Courty, Opt. Commun. 115, 199 (1995).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. A (1)

J. W. R. Tabosa, S. S. Vianna, and F. A. M. de Oliveira, Phys. Rev. A 55, 2968 (1997).
[CrossRef]

Phys. Rev. Lett. (5)

E. L. Raab, M. Prentiss, A. Cable, S. Chu, and D. E. Pritchard, Phys. Rev. Lett. 59, 2631 (1987).
[CrossRef] [PubMed]

J. W. R. Tabosa, G. Chen, Z. Hu, R. B. Lee, and H. J. Kimble, Phys. Rev. Lett. 66, 3245 (1991).
[CrossRef] [PubMed]

J.-F. Roch, K. Vigneron, Ph. Grelu, A. Sinatra, J.-Ph. Poizat, and Ph. Grangier, Phys. Rev. Lett. 78, 634 (1997).
[CrossRef]

This FWM should be distinguished from Bragg diffraction in optical lattices, in which the atoms are confined to only the lattice points; see, for example, G. Raithel, G. Birkl, A. Kastberg, W. D. Phillips, and S. L. Rolston, Phys. Rev. Lett. 78, 630 (1997).
[CrossRef]

P. D. Lett, R. N. Watts, C. I. Westbrook, W. D. Phillips, P. L. Gould, and H. J. Metcalf, Phys. Rev. Lett. 61, 169 (1988).
[CrossRef] [PubMed]

Other (3)

R. M. Macfarlane and R. M. Shelby, in Spectroscopy of Solids Containing Rare Earth Ions, A. A. Kaplyanskii and R. M. Macfarlane, eds. (North-Holland, Amsterdam, 1987).

The ?10?cm mean free path of the Na atom in a MOT is much larger than the cloud size.?Also, the effects of the forces of gravity and the ?10?G/cm magnetic-field gradient on atoms in a MOT are both negligible at the time scale of interest.

See, for example, H. J. Eichler, P. Günter, and D. W. Pohl, Laser-Induced Gratings (Springer-Verlag, Berlin, 1986).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Schematic of the experimental setup: PMT, photomultiplier tube; DFWM, degenerate four-wave mixing; att., attenuator. Bottom: pulse-timing sequence of the trap (repump) beams, the pump beams, and the probe beam. Inset: the relevant energy levels of the Na atoms.

Fig. 2
Fig. 2

CCD camera image of the three excitation beams and the FWM signal.

Fig. 3
Fig. 3

(a) FWM signal intensity as a function of the pump-pulse width (pump power, 500 µW for filled circles, 250 µW for open circles) and the best-fit theoretical curves (solid curves).

Fig. 4
Fig. 4

(a) FWM signal intensity as a function of the probe-pulse delay time (open circles) and the best-fit theoretical curve (solid curve). (b) Probe transmission signal as a function of the probe-pulse delay time.

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

n2x, 0=N exp-2ξ cos2kgx=N exp-ξI0ξ-2I1ξcos2kgx+,
n2x, t=1uπ1/2dvx exp-vx2u2n2x-vxt, 0,
SFWMtN2 exp-2ξI12ξexp-t/τD2.
τD=d2πu=d2πm2kBT,

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